<h2>题目编号 : 123</h2>
<div style="color:#666;font-size:80%;">16 June 2006</div><br />
<div class="problem_content">

<p>Let <i>p</i><img src="" style="display:none;" alt="_(" /><sub>n</sub><img src="" style="display:none;" alt=")" /> be the <i>n</i>th prime: 2, 3, 5, 7, 11, ..., and let <i>r</i> be the remainder when (<i>p</i><img src="" style="display:none;" alt="_(" /><sub>n</sub><img src="" style="display:none;" alt=")" /><img src='images/symbol_minus.gif' width='9' height='3' alt='&minus;' border='0' style='vertical-align:middle;' />1)<img src="" style="display:none;" alt="^(" /><sup><i>n</i></sup><img src="" style="display:none;" alt=")" /> + (<i>p</i><img src="" style="display:none;" alt="_(" /><sub>n</sub><img src="" style="display:none;" alt=")" />+1)<img src="" style="display:none;" alt="^(" /><sup><i>n</i></sup><img src="" style="display:none;" alt=")" /> is divided by <i>p</i><img src="" style="display:none;" alt="_(" /><sub>n</sub><img src="" style="display:none;" alt=")" /><img src="" style="display:none;" alt="^(" /><sup>2</sup><img src="" style="display:none;" alt=")" />.</p>
<p>For example, when <i>n</i> = 3, <i>p</i><img src="" style="display:none;" alt="_(" /><sub>3</sub><img src="" style="display:none;" alt=")" /> = 5, and 4<img src="" style="display:none;" alt="^(" /><sup>3</sup><img src="" style="display:none;" alt=")" /> + 6<img src="" style="display:none;" alt="^(" /><sup>3</sup><img src="" style="display:none;" alt=")" /> = 280 <img src='images/symbol_cong.gif' width='9' height='11' alt='&equiv;' border='0' style='vertical-align:middle;' /> 5 mod 25.</p>
<p>The least value of <i>n</i> for which the remainder first exceeds 10<img src="" style="display:none;" alt="^(" /><sup>9</sup><img src="" style="display:none;" alt=")" /> is 7037.</p>
<p>Find the least value of <i>n</i> for which the remainder first exceeds 10<img src="" style="display:none;" alt="^(" /><sup>10</sup><img src="" style="display:none;" alt=")" />.</p>

</div><br />
